A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is
Explanation:
4 liters out of 40 liters is remvoed, hence 4/40 = 1/10th is removed every time. ∴ 1 - 1/10 = 9/10th remains every time.
Quantity of milk will become less than that of water as soon as quantity of milk goes below 20 liters.
∴ Quantity of milk remaining after n replacements = 40 × (9/10)n < 20 ⇒ (0.9)n < 0.5
Least value of n satisfying above inequality is 7.
Hence, 7.
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